Quasistationarity of continuous-time Markov chains with positive drift

We shall study continuous-time Markov chains on the nonnegative integers which are both irreducible and transient, and which exhibit discernible stationarity before drift to infinity sets in. We will show how this 'quasi' stationary behaviour can be modelled using a limiting conditional distribution: specifically, the limiting state probabilities conditional on not having left 0 for the last time. By way of a dual chain, obtained by killing the original process on last exit from 0, we invoke the theory of quasistationarity for absorbing Markov chains. We prove that the conditioned state probabilities of the original chain are equal to the state probabilities of its dual conditioned on non-absorption, thus allowing us to establish the simultaneous existence and then equivalence, of their limiting conditional distributions. Although a limiting conditional distribution for the dual chain is always a quasistationary distribution in the usual sense, a similar statement is not possible for the original chain.

Further results on the relationship between mu-invariant measures and quasi-stationary distributions for absorbing continuous-time Markov chains

This note considers continuous-time Markov chains whose state space consists of an irreducible class, C, and an absorbing state which is accessible from C. The purpose is to provide results on mu-invariant and mu-subinvariant measures where absorption occurs with probability less than one. In particular, the well-known premise that the mu-invariant measure, m, for the transition rates be finite is replaced by the more natural premise that m be finite with respect to the absorption probabilities. The relationship between mu-invariant measures and quasi-stationary distributions is discussed. (C) 2000 Elsevier Science Ltd. All rights reserved.

Metal-directed synthesis routes to a 16-membered tetraazamacrocycle with two pendant primary amine groups

The reaction of the bis(propane-1,3-diamine)copper(II) ion with paraformaldehyde and nitroethane in dry methanol under basic conditions produces a macrocyclic product, (cis-3,11-dimethyl-3,11-dinitro-1,5,9,13-tetraazacyclohexadecane)copper(II) perchlorate, in low yield, compared with the good yield obtained in the parallel chemistry possible even under aqueous conditions using palladium(II) as a template. The palladium complex was reduced with zinc amalgam in dilute aqueous acid to yield the metal-free 16-membered macrocyclic hexaamine, in this case re-complexed and characterised by an X-ray crystal structure as the (cis-3,11-dimethyl-1,5,9,13-tetraazacyclohexadecane-3,11-diamine)copper(II) perchlorate. The copper ion is found in a tetragonally elongated and trigonally-distorted octahedral environment, with all six of the ligand nitrogens coordinated, the two primary amine pendant groups occupying cis sites. (C) 2000 Elsevier Science S.A. All rights reserved.

Robust Mixture Modelling Using the t Distribution

Normal mixture models are being increasingly used to model the distributions of a wide variety of random phenomena and to cluster sets of continuous multivariate data. However, for a set of data containing a group or groups of observations with longer than normal tails or atypical observations, the use of normal components may unduly affect the fit of the mixture model. In this paper, we consider a more robust approach by modelling the data by a mixture of t distributions. The use of the ECM algorithm to fit this t mixture model is described and examples of its use are given in the context of clustering multivariate data in the presence of atypical observations in the form of background noise.

Participation in recreational physical activity: Why do socioeconomic groups differ?

This qualitative study explored how influences on recreational physical activity (RPA) were patterned by socioeconomic position. Face-to-face interviews were conducted with 10 males and 10 females in three socioeconomic groups (N = 60). Influences salient across all groups included previous opportunities, physical health, social assistance, safety, environmental aesthetics and urban design, physical and health benefits, and barriers of self-consciousness, low skill, and weather/time of year. Influences more salient to the high socioeconomic group included social benefits, achieving a balanced lifestyle, and the barrier of an unpredictable lifestyle. Influences more salient to the high and mid socioeconomic groups included efficacy, perceived need, activity demands, affiliation, emotional benefits, and the barrier of competing demands. Influences more salient to the low socioeconomic group included poor health and barriers of inconvenient access and low personal functioning. Data suggest that efforts to increase RPA in the population should include both general and socioeconomically targeted strategies.

Non-diagonal solutions of the reflection equation for the trigonometric A((1)) (n-1) vertex model

We obtain a class of non-diagonal solutions of the reflection equation for the trigonometric A(n-1)((1)) vertex model. The solutions can be expressed in terms of intertwinner matrix and its inverse, which intertwine two trigonometric R-matrices. In addition to a discrete (positive integer) parameter l, 1 less than or equal to l less than or equal to n, the solution contains n + 2 continuous boundary parameters.

(Review) Body mass index and risk of diabetes mellitus in the Asia-Pacific region

Few prospective data from the Asia Pacific region are available relating body mass index to the risk of diabetes. Our objective was to provide reliable age, sex and region specific estimates of the associations between body mass index and diabetes. Twenty-seven cohort studies from Asia, New Zealand and Australia, including 154,989 participants, contributed 1,244,793 person-years of follow-up. Outcome data included a combination of incidence of diabetes (based on blood glucose measurements) and fatal diabetes events. Hazard ratios were calculated from Cox models, stratified by sex and cohort, and adjusted for age at risk and smoking. During follow-up (mean = 8 years), 75 fatal diabetes events and 242 new cases of diabetes were documented. There were continuous positive associations between baseline body mass index and risk of diabetes with each 2 kg/m(2) lower body mass index associated with a 27% (23-30%) lower risk of diabetes. The associations were stronger in younger age groups, and regional comparisons demonstrated slightly stronger associations in Asian than in Australasian cohorts (P = 0.04). This overview provides evidence of a strong continuous association between body mass index and diabetes in the Asia Pacific region. The results indicate considerable potential for reduction in incidence of diabetes with population-wide lowering of body mass index in this region.

Discrete and continuous models for dry masonry columns

The dynamic response of dry masonry columns can be approximated with finite-difference equations. Continuum models follow by replacing the difference quotients of the discrete model by corresponding differential expressions. The mathematically simplest of these models is a one-dimensional Cosserat theory. Within the presented homogenization context, the Cosserat theory is obtained by making ad hoc assumptions regarding the relative importance of certain terms in the differential expansions. The quality of approximation of the various theories is tested by comparison of the dispersion relations for bending waves with the dispersion relation of the discrete theory. All theories coincide with differences of less than 1% for wave-length-block-height (L/h) ratios bigger than 2 pi. The theory based on systematic differential approximation remains accurate up to L/h = 3 and then diverges rapidly. The Cosserat model becomes increasingly inaccurate for L/h < 2 pi. However, in contrast to the systematic approximation, the wave speed remains finite. In conclusion, considering its relative simplicity, the Cosserat model appears to be the natural starting point for the development of continuum models for blocky structures.

Children's cooperative behavior and interactions in trained and untrained work groups in regular classrooms

This study examined group and individual factors that facilitate changes in cooperation and learning outcomes in trained and untrained work groups of elementary school-age children. The study had two foci. The first was to determine if the cooperative behaviors and interactions of children in classroom groups who were trained in cooperative learning skins were different from those of children who were given no training, and the second was to investigate small group interactions and achievement in these groups over time. The results showed that there were observable differences between student interactions in the two conditions and these differences were maintained over time. Compared with children in the untrained groups, those in the trained groups were consistently more cooperative and helpful to each other; they actively tried to involve each other in the learning task by using language which was more inclusive (e.g., frequent use of ''we''), and they gave more explanations to assist each other as they worked together. It appeared that as the children worked together over time, they became more responsive to the learning needs of each other. Furthermore, the children in the trained groups performed significantly better on the learning outcomes questionnaire than those in the untrained groups. (C) 1997 Society for the Study of School Psychology. Published by Elsevier Science Ltd.

A high-resolution genetic map of the familial Mediterranean fever candidate region allows identification of haplotype-sharing among ethnic groups

Familial Mediterranean fever (FMF) is a recessive disorder of inflammation caused by mutations in a gene (designated MEFV) on chromosome 16p13.3, We have recently constructed a 1-Mb cosmid contig that includes the FMF critical region. Here we show genotype data for 12 markers from our physical map, including 5 newly identified microsatellites, in FMF families. Intrafamilial recombinations placed MEFV in the similar to 285 kb between D16S468/D16S3070 and D16S3376. We observed significant linkage disequilibrium in the North African Jewish population, and historical recombinants in the founder haplotype placed MEFV between D16S3082 and D16S3373 (similar to 200 kb). In smaller panels of Iraqi Jewish, Arab, and Armenian families, there were significant allelic associations only for D16S3370 and D16S2617 among the Armenians. A sizable minority of Iraqi Jewish and Armenian carrier chromosomes appeared to be derived from the North African Jewish ancestral haplotype. We observed a unique FMF haplotype common to Iraqi Jews, Arabs, and Armenians and two other haplotypes restricted to either the Iraqi Jewish or the Armenian population. These data support the view that a few major mutations account for a large percentage of the cases of FMF and suggest that same of these mutations arose before the affected Middle Eastern populations diverged from one another. (C) 1997 Academic Press.

Genetic algorithms for continuous optimization problems - a concept of parameter-space size adjustment

The concept of parameter-space size adjustment is pn,posed in order to enable successful application of genetic algorithms to continuous optimization problems. Performance of genetic algorithms with six different combinations of selection and reproduction mechanisms, with and without parameter-space size adjustment, were severely tested on eleven multiminima test functions. An algorithm with the best performance was employed for the determination of the model parameters of the optical constants of Pt, Ni and Cr.